Explanation It is known that if an expression is in the form of p ( x ) q ( x ) , where p ( x ) and q ( x ) are polinomials , then it is said to be a rational function. Vertical asymptotes of a function occur when the denominator of the function gets zero. It is given that the function has vertical asymptote at x = − 1 . So, the denominator of the function must be x − ( − 1 ) that is x = 1 . It is given that the function has vertical asymptote at x = 2 . So, the denominator of the function must be x − 2 that is x = − 2 . Again given that the x -intercept is ( − 4 , 0 ) . So, the numerator of the function must be x − ( − 4 ) that is x = 4 . Thus, the rational function satisfying the above conditions is f ( x ) = x + 4 ( x + 1 ) ( x − 2 )

College Algebra: Graphs and Models (6th Edition)

6th Edition

ISBN: 9780134179032

Author: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 4, Problem 26T

To determine

The rational function which have the vertical asymtotes x=−1 and x=2 and x-intercept is (−4,0).

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4, Problem 25T

Chapter 4, Problem 27T

Students have asked these similar questions

Q1: A: Let M and N be two subspace of finite dimension linear space X, show that if M = N then dim M = dim N but the converse need not to be true. B: Let A and B two balanced subsets of a linear space X, show that whether An B and AUB are balanced sets or nor. Q2: Answer only two A:Let M be a subset of a linear space X, show that M is a hyperplane of X iff there exists ƒ€ X'/{0} and a € F such that M = (x = x/f&x) = x}. fe B:Show that every two norms on finite dimension linear space are equivalent C: Let f be a linear function from a normed space X in to a normed space Y, show that continuous at x, E X iff for any sequence (x) in X converge to Xo then the sequence (f(x)) converge to (f(x)) in Y. Q3: A:Let M be a closed subspace of a normed space X, constract a linear space X/M as normed space B: Let A be a finite dimension subspace of a Banach space X, show that A is closed. C: Show that every finite dimension normed space is Banach space.

• Plane II is spanned by the vectors: P12 P2 = 1 • Subspace W is spanned by the vectors: W₁ = -- () · 2 1 W2 = 0

Three streams - Stream A, Stream B, and Stream C - flow into a lake. The flow rates of these streams are not yet known and thus to be found. The combined water inflow from the streams is 300 m³/h. The rate of Stream A is three times the combined rates of Stream B and Stream C. The rate of Stream B is 50 m³/h less than half of the difference between the rates of Stream A and Stream C. Find the flow rates of the three streams by setting up an equation system Ax = b and solving it for x. Provide the values of A and b. Assuming that you get to an upper-triangular matrix U using an elimination matrix E such that U = E A, provide also the components of E.

Chapter 4 Solutions

College Algebra: Graphs and Models (6th Edition)

Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 2E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 10E

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The rational function which have the vertical asymtotes x = − 1 and x = 2 and x -intercept is ( − 4 , 0 ) .

Solution Summary: The author explains the rational function which has vertical asymtotes and x -intercept, which is (-4,0).

Videos

The rational function which have the vertical asymtotes x=−1 and x=2 and x-intercept is (−4,0).

Want to see the full answer?

Chapter 4 Solutions